Abstract
We present an approach to understanding the origin of inertia involving the electromagnetic component of the quantum vacuum and propose this as a step toward an alternative to Mach's principle. Preliminary analysis of the momentum flux of the classical electromagnetic zero-point radiation impinging on accelerated objects as viewed by an inertial observer suggests that the resistance to acceleration attributed to inertia may be at least in part a force of opposition originating in the vacuum. This analysis avoids the ad hoc modeling of particle-field interaction dynamics used previously by Haisch, Rueda, and Puthoff (Phys. Rev. A 49, 678, (1994)) to derive a similar result. This present approach is not dependent upon what happens at the particle point, but on how an external observer assesses the kinematical characteristics of the zero-point radiation impinging on the accelerated object. A relativistic form of the equation of motion results from the present analysis. Its manifestly covariant form yields a simple result that may be interpreted as a contribution to inertial mass. We note that our approach is related by the principle of equivalence to Sakharov's conjecture (Sov. Phys. Dokl. 12, 1040, (1968)) of a connection between Einstein action and the vacuum. The argument presented may thus be construed as a descendant of Sakharov's conjecture by which we attempt to attribute a mass-giving property to the electromagnetic component—and possibly other components—of the vacuum. In this view the physical momentum of an object is related to the radiative momentum flux of the vacuum instantaneously contained in the characteristic proper volume of the object. The interaction process between the accelerated object and the vacuum (akin to absorption or scattering of electromagnetic radiation) appears to generate a physical resistance (reaction force) to acceleration suggestive of what has been historically known as inertia.
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For P µto be a four-vector, the four-divergence of the electromagnetic energy momentum stress tensor should vanish, ¶ ∂ µ \(\Theta ^{\mu \nu } \)= 0. As the only interaction considered in this work is the electromagnetic and as explicitly we omit any other components of the vacuum besides the electromagnetic, there is no question that the stress tensor \(\Theta ^{\mu \nu } \) is purely electromagnetic. In more complex models where there are other interactions it would be the four-divergence of the sum of the electromagnetic and the other field stress tensor (Poincaréstress) that should vanish, i.e., ¶ ∂ µ \({\text{(}}\Theta ^{\mu \nu } + \Theta _{other}^{\mu \nu } )\) = 0. In such a case it becomes a matter of choice if individually ¶ ∂ µ \(\Theta ^{\mu \nu } \) and ¶ ∂ µ \(\Theta _{other}^{\mu \nu } \) each separately vanishes or not, and their divergences are then just the opposites of each other. A nice discussion of this point is found in I. Campos and J. L. Jiménez, Phys. Rev. D 33, 607 (1986). See also I. Campos and J. L. Jiménez, Eur. J. Phys. 13, 177 (1992). T. H. Boyer, Phys. Rev. D 25, 3246 (1982); Phys. Rev. D 25, 3251 (1982). So when there are other fields (interactions), the electromagnetic four-vector character of P µis not that compelling, but in the present purely electromagnetic case such four-vector character necessarily holds since ¶ ∂ µ \(\Theta ^{\mu \nu } \) = 0. In the pure electromagnetic case which for simplicity of treatment we assume here, the 4/3 factor becomes unity. If, on the other hand, we were to assume other fields (e.g., those participating in the ŋ(ω) response of the particle), then the obliteration of the 4/3 factor becomes more a matter of theoretical preference.
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Rueda, A., Haisch, B. Contribution to Inertial Mass by Reaction of the Vacuum to Accelerated Motion. Foundations of Physics 28, 1057–1108 (1998). https://doi.org/10.1023/A:1018893903079
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DOI: https://doi.org/10.1023/A:1018893903079